What is the average of even numbers from 7 to 113? Here we will show you how to calculate the average of even numbers from 7 to 113.
To find the average of the even numbers from 7 to 113, we first calculate how many even numbers there are from 7 to 113. Then, we calculate the sum of even numbers from 7 to 113. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 7 to 113, and the even numbers within that range are from 8 to 112. Therefore, the first even number in the sequence is 8, and the last even number in the sequence is 112.
Step 1) Calculate the total number of even numbers from 7 to 113
Here we calculate the total number of even numbers from 7 to 113 by entering the first and last even number in the sequence into our formula. Here is the formula and the math:
tot = (last - first + 2) ÷ 2
tot = (112 - 8 + 2) ÷ 2
tot = 106 ÷ 2
tot = 53
Total even numbers from 7 to 113 = 53
Step 2) Calculate the sum of even numbers from 7 to 113
To calculate the sum of even numbers from 7 to 113, you enter the total even numbers (tot) from Step 1 and the first even number in the sequence into our formula. Here is the formula and the math:
sum = (tot ÷ 2) × (2 × first + (2 × (tot - 1))
sum = (53 ÷ 2) × (2 × 8 + (2 × (53 - 1))
sum = 26.5 × (16 + 104)
sum = 26.5 × 120
sum = 3180
Sum of even numbers from 7 to 113 = 3180
Step 3) Calculate the average of even numbers from 7 to 113
Almost done! Now we can calculate the average of even numbers from 7 to 113 by dividing the sum of even numbers from Step 2 by the total even numbers from Step 1. Here is the formula, the math, and the answer:
Average = sum ÷ tot
Average = 3180 ÷ 53
Average = 60
Average of even numbers from 7 to 113 = 60
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.